TY - JOUR

T1 - On the average-case complexity of parameterized clique

AU - Fountoulakis, Nikolaos

AU - Friedrich, Tobias

AU - Hermelin, Danny

N1 - Funding Information:
The research leading to these results has received funding from the German Research Foundation ( DFG ) and the German–Israeli Foundation for Scientific Research and Development (GIF).
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The κ-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems. Moreover, its average-case complexity analysis has created a long thread of research already since the 1970s. Here, we continue this line of research by studying the dependence of the average-case complexity of the κ-Clique problem on the parameter k. To this end, we define two natural parameterized analogs of efficient average-case algorithms. We then show that k-Clique admits both analogues for Erdős-Rényi random graphs of arbitrary density. We also show that κ-Clique is unlikely to admit either of these analogs for some specific computable input distribution.

AB - The κ-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems. Moreover, its average-case complexity analysis has created a long thread of research already since the 1970s. Here, we continue this line of research by studying the dependence of the average-case complexity of the κ-Clique problem on the parameter k. To this end, we define two natural parameterized analogs of efficient average-case algorithms. We then show that k-Clique admits both analogues for Erdős-Rényi random graphs of arbitrary density. We also show that κ-Clique is unlikely to admit either of these analogs for some specific computable input distribution.

KW - Average-case

KW - Clique

KW - Computational complexity

KW - Parameterized complexity

UR - http://www.scopus.com/inward/record.url?scp=84930248233&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2015.01.042

DO - 10.1016/j.tcs.2015.01.042

M3 - Article

AN - SCOPUS:84930248233

VL - 576

SP - 18

EP - 29

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1

ER -